Numerical analysis of Lavrentiev-regularized state constrained elliptic control problems
- Hinze, Michael
- Meyer, Christian
2010 Mathematics Subject Classification
- 49K20 49N10 49M20
- Optimal control of elliptic equations, quadratic programming, pointwise state constraints, mixed constraints, Lavrentiev regularization
In the present work, we apply semi-discretization proposed by the first author in  to Lavrentiev-regularized state constrained elliptic control problems. We extend the results of  and prove weak convergence of the adjoint states and multipliers of the regularized problems to their counterparts of the original problem. Further, we prove error estimates for finite element discretizations of the regularized problem and investigate the overall error imposed by the finite element discretization of the regularized problem compared to the continuous solution of the original problem. Finally we present numerical results which confirm our analytical findings.